3. PQR is an isosceles triangle with PQ = PR, and angle QPR = x". P
Angle PQR = (2x + 30)
Diagram not drawn to scale
PR = (2x + 3) cm
QR = (r + 3) cm
1(2r+3)
H
+
(2x +30)
R
(r+3)
(a) Find an expression for the perimeter of the triangle in terms of r, giving
your answer in its simplest form.
(b) Work out the value of r, if the perimeter is 49 cm.

a). Perimeter = (5r + 9) cm

b). r = 8

Step-by-step explanation:

Property of isosceles triangle:

- Two sides of an isosceles triangle are equal.

- Opposite sides of the equal angles are equal in measure.

  From the figure attached,

  PQ = QR = (2r + 3)

a). Since perimeter of a polygon = sum of all sides of the polygon

                                                 = PQ + QR + PR

                                                 = (2r + 3) + (2r + 3) + (r + 3)

                                                 = 5r + 9

    Perimeter of the given triangle = (5r + 9) cm

b). Perimeter of the given triangle = 49 cm

    (5r + 9) = 49

     5r = 40

      r = 8

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